Endpoint $L^p-L^q$ estimates for degenerate Radon transforms in ${\mathbb R}^2$ associated with real-analytic functions

Abstract. We consider degenerate Radon transforms of the form

$Rf(t,x)=\int_{\mathbb R} f(t+S(x,y),y)\psi(x,y)dy$

where $\psi$ is supported in a small neighborhood of the origin. Under the condition that S is real-analytic, we prove complete $L^p-L^q$ estimates for R.